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On Predictability and Profitability: Would AI induced Trading Rules be Sensitive to the Entropy On Predictability and Profitability: Would AI induced Trading Rules be Sensitive to the Entropy of time Series Nicolas NAVET INRIA – France [email protected] fr Shu-Heng. CHEN – AIECON/NCCU Taiwan [email protected] edu. tw 09/04/2008

Outline Outline

Estimating entropy Estimating entropy

Selected estimator ^ h. SM = ¤i à 1 n X ! ¡ n Selected estimator ^ h. SM = ¤i à 1 n X ! ¡ n ¤i 1 log n 2 i= 1 : length of the shortest string that does not appear in the i previous symbols Example: 0 1 1 0 0 ¤ 6 = 3

Performance of the estimator = ¡ P 8 i=1 1=8 log p = 3 Performance of the estimator = ¡ P 8 i=1 1=8 log p = 3 b. p. c. 2 ^ h. SM = 2: 96 ^ h. SM = 2: 77 ¸ 2: 99

Preprocessing the data (1/2) rt = ln( f g 2 !f g 2 R Preprocessing the data (1/2) rt = ln( f g 2 !f g 2 R N rt At 3, 4, 1, 0, 2, 6, 2, … ) pt pt ¡ 1

Preprocessing the data (2/2) Preprocessing the data (2/2)

Entropy of NYSE US 100 stocks – period 2000 -2006 Mean = Median = Entropy of NYSE US 100 stocks – period 2000 -2006 Mean = Median = 2. 75 Max = 2. 79 Min = 2. 68 Rand() boost = 2. 9 NB : a normal distribution of same mean and standard deviation is plotted for comparison.

Entropy is high but price time series are not random! Original time series Randomly Entropy is high but price time series are not random! Original time series Randomly shuffled time series

Stocks under study Highest entropy time series Lowest entropy time series Symbol OXY VLO Stocks under study Highest entropy time series Lowest entropy time series Symbol OXY VLO MRO BAX WAG Entropy 2: 789 2: 787 2: 785 2: 78 2: 776 Symbol TWX EMC C JPM GE Entropy 2: 677 2: 694 2: 712 2: 716 2: 723

BDS tests: are daily log price changes i. i. d ? m 2 3 BDS tests: are daily log price changes i. i. d ? m 2 3 5 ± 1 1 1 Lowest entropy time series TWX 18. 06 22. 67 34. 18 EM C 14. 21 19. 54 29. 17 C 13. 9 18. 76 28. 12 JP M 11. 82 16. 46 26. 80 Highest V LO entropy time series OXY M RO BAX 5. 66 6. 61 9. 04 4. 17 5. 35 6. 88 6. 69 9. 40 13. 08 8. 13 11. 11 15. 31 GE 11. 67 16. 34 24. 21 W AG 7. 45 8. 89 11. 17

Autocorrelation analysis High entropy stock (OXY) Low entropy stock (C) Autocorrelation analysis High entropy stock (OXY) Low entropy stock (C)

Part 2 : does low entropy imply better profitability of TA? Addressed here: are Part 2 : does low entropy imply better profitability of TA? Addressed here: are GP-induced rules more efficient on low-entropy stocks ?

GP : the big picture Training interval Validation interval 1 ) Creation of the GP : the big picture Training interval Validation interval 1 ) Creation of the Further selection trading rules using on unseen data GP 2) Selection of the One strategy is best resulting chosen for outstrategies of-sample 2000 2002 2004 Out-of-sample interval Performance evaluation 2006

GP performance assessment GP performance assessment

Experimental setup Experimental setup

Results: high entropy stocks OXY V LO M RO BAX W AG GP net Results: high entropy stocks OXY V LO M RO BAX W AG GP net pro¯ts 15: 5 K$ 7 K$ 15 K$ 24 K$ 6 K$ LT net pro¯ts 14 K$ 11: 5 K$ 18: 5 K$ 13 K$ ¡ 0: 5 K$ GP>LT? No No No Yes LT>GP? No No No GP is always profitable LT is never better than GP (at a 95% confidence level) GP outperforms LT 2 times out of 5 (at a 95% confidence level)

Results: low entropy stocks TWX EM C C JP M GE GP net pro¯ts Results: low entropy stocks TWX EM C C JP M GE GP net pro¯ts ¡ ¡ 9 K$ 16: 5 K$ 15 K$ ¡ 6 K$ 0: 5 K$ LT ¡ pro¯ts net ¡ 1: 5 K$ 11 K$ 18: 5 K$ 10 K$ 0: 5 K$ GP>LT? No No No LT>GP? Yes No No No GP is never better than LT (at a 95% confidence level) LT outperforms GP 2 times out of 5 (at a 95% confidence level)

Explanations (1/2) Typical low entropy stock (EMC) 2000 2006 Explanations (1/2) Typical low entropy stock (EMC) 2000 2006

Explanations (2/2) BAX WAG Explanations (2/2) BAX WAG

Conclusions Conclusions

Perspectives Perspectives

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